Class 12 Physics Numericals — 20 Most Repeated Types With Shortcuts 2027
20 most repeated Class 12 Physics numerical problem types for board exam 2027. Electrostatics, Current Electricity, Optics, Modern Physics, EMI, Magnetism — typical problem setup, formula, shortcut method, common mistakes, and marks allocation. Based on PYQ analysis 2024-2026.
In short: Physics numericals carry 25-30 marks in the CBSE Class 12 board paper. These are not random problems — the same 20 types rotate every year. Coulomb's Law, Kirchhoff's rules, lens formula, photoelectric effect, de Broglie wavelength, nuclear reactions — these appear in 3 out of 3 papers (2024-2026). For each type below: the typical problem setup, the formula to use, a shortcut method that saves time, common mistakes that cost marks, and the marks allocation. Master these 20 types and you secure 25+ marks in Physics.
How This List Was Built
Source
What We Analysed
CBSE SQP 2027
Numerical question types and mark distribution
PYQ 2024, 2025, 2026
Actual board papers. Tracked which numerical types appeared each year.
CBSE Marking Scheme
Step-wise marks — shows exactly how many marks each formula/step earns.
NCERT Solved Examples
The board picks numerical types directly from NCERT examples.
Two charges q₁ and q₂ are placed r cm apart. Find the force between them. OR: Find the distance at which force becomes a given fraction.
Formula
F = kq₁q₂/r² where k = 9 × 10⁹ Nm²/C²
Shortcut
If charges are in μC, convert: 1 μC = 10⁻⁶ C. If distance in cm, convert to m. Write F = 9 × 10⁹ × q₁ × q₂ / r² directly.
Common Mistake
Forgetting to convert μC to C or cm to m. Wrong power of 10 → wrong answer.
Marks
2-3 marks
PYQ Frequency
3/3 years (2024-2026)
Step-wise marks:
Step
Marks
Write the formula
0.5
Substitute values (with correct units)
1
Calculate and simplify
0.5-1
Final answer with unit (N)
0.5
#2. Electric Field Due to a Point Charge / System of Charges
Element
Detail
Typical Problem
Find the electric field at a point P due to a charge q at distance r. OR: Find the point where net electric field is zero between two charges.
Formula
E = kq/r² (for point charge). For net E = 0: E₁ = E₂ → kq₁/x² = kq₂/(d-x)²
Shortcut
For "where is E = 0" between two charges: x/d = √q₁ / (√q₁ + √q₂). For same-sign charges, the point is between them. For opposite-sign charges, it is outside.
Common Mistake
Confusing "between charges" vs "outside." For same-sign → point is between. For opposite-sign → point is outside (near the smaller charge).
Marks
2-3 marks
PYQ Frequency
2/3 years
#3. Electric Potential and Potential Energy
Element
Detail
Typical Problem
Find the potential at a point due to a system of charges. OR: Calculate the work done in moving a charge from point A to B.
Formula
V = kq/r (potential). U = kq₁q₂/r (potential energy). W = q(V_A - V_B)
Shortcut
Potential is scalar — just add (no vector addition). If charges are on vertices of a triangle/square, add V = kq₁/r₁ + kq₂/r₂ + ... directly.
Common Mistake
Treating potential as a vector (it is a scalar). Forgetting the sign of the charge when calculating V.
Marks
2-3 marks
PYQ Frequency
3/3 years
#4. Capacitance — Series/Parallel Combination
Element
Detail
Typical Problem
Find the equivalent capacitance of a given combination. OR: Find charge/voltage across each capacitor.
For 2 capacitors in series: C_eq = C₁C₂/(C₁+C₂). In series, charge is same. In parallel, voltage is same.
Common Mistake
Confusing series/parallel rules for capacitors with resistors (they are OPPOSITE). Capacitors in series: 1/C formula (like resistors in parallel).
Marks
2-3 marks
PYQ Frequency
2/3 years
Current Electricity — Numericals #5-7
#5. Kirchhoff's Rules — Circuit Problems
Element
Detail
Typical Problem
Given a circuit with 2-3 loops and multiple resistors/batteries. Find the current through each branch.
Formula
Junction rule: ΣI = 0 (current in = current out). Loop rule: ΣV = 0 (sum of voltages around a loop = 0).
Shortcut
Assign current directions (guess). If the answer is negative, the direction is opposite. Set up 2 equations for 2 unknowns. Solve simultaneously.
Common Mistake
Wrong sign convention. Going through a battery from - to + = +EMF. Going through a resistor in the direction of current = -IR.
Marks
3-5 marks
PYQ Frequency
3/3 years
Step-wise marks (5-mark question):
Step
Marks
Draw the circuit with current directions labelled
0.5
Apply junction rule
0.5
Apply loop rule for loop 1
1
Apply loop rule for loop 2
1
Solve equations for I₁, I₂, I₃
1.5
Final answer with direction
0.5
#6. Wheatstone Bridge / Meter Bridge
Element
Detail
Typical Problem
In a meter bridge, the balance point is at l cm from one end. Find the unknown resistance. OR: Verify balance condition.
Formula
R/S = l/(100-l). Balance condition for Wheatstone: P/Q = R/S.
Shortcut
Meter bridge is just a Wheatstone bridge. If balance point shifts, use R = S × l/(100-l). For sensitivity questions, balance point should be near 50 cm.
Common Mistake
Mixing up which resistance corresponds to which length. R corresponds to length l on its side.
Marks
2-3 marks
PYQ Frequency
2/3 years
#7. Internal Resistance and EMF — Potentiometer
Element
Detail
Typical Problem
A cell of EMF E and internal resistance r is connected to an external resistance R. Find the current, terminal voltage, or power. OR: Using potentiometer, find EMF of a cell.
Formula
I = E/(R+r). Terminal voltage V = E - Ir. Potentiometer: E₁/E₂ = l₁/l₂
Shortcut
Terminal voltage = EMF only when no current flows (open circuit). When current flows, V < E always.
Common Mistake
Forgetting internal resistance. Writing I = E/R instead of I = E/(R+r). This is the most common error in current electricity.
Marks
2-3 marks
PYQ Frequency
3/3 years
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#8. Force on a Current-Carrying Conductor / Moving Charge in Magnetic Field
Element
Detail
Typical Problem
A wire of length L carrying current I is placed in a magnetic field B at angle θ. Find the force. OR: A charged particle enters a magnetic field. Find force/radius.
Formula
Wire: F = BILsinθ. Charged particle: F = qvBsinθ. Radius of circular path: r = mv/(qB)
Shortcut
F is maximum when θ = 90° (perpendicular). F = 0 when θ = 0° (parallel). For circular motion, the time period T = 2πm/(qB) — independent of velocity.
Common Mistake
Using θ = 0 when the field and wire are perpendicular (θ should be 90°). Confusing the direction using Fleming's left-hand rule.
Marks
2-3 marks
PYQ Frequency
3/3 years
#9. Biot-Savart Law — Magnetic Field at Centre of a Coil
Element
Detail
Typical Problem
Find the magnetic field at the centre of a circular coil of N turns, radius r, carrying current I.
Formula
B = μ₀NI/(2r) at the centre. On the axis at distance x: B = μ₀NIr²/[2(r²+x²)^(3/2)]
Shortcut
At the centre (x = 0): formula simplifies to B = μ₀NI/(2r). If N doubles, B doubles. If r doubles, B halves.
Common Mistake
Forgetting N (number of turns). Using diameter instead of radius. Missing μ₀ = 4π × 10⁻⁷.
Marks
2-3 marks
PYQ Frequency
2/3 years
#10. Ampere's Circuital Law — Solenoid / Toroid
Element
Detail
Typical Problem
A solenoid of N turns, length L, carrying current I. Find B inside the solenoid.
Formula
B = μ₀nI where n = N/L (turns per unit length). Toroid: B = μ₀NI/(2πr)
Shortcut
Solenoid: B is uniform inside and zero outside (ideal). Toroid: B exists only inside the ring.
Common Mistake
Using N instead of n = N/L. Confusing solenoid and toroid formulas.
Marks
2-3 marks
PYQ Frequency
2/3 years
EMI & AC — Numericals #11-12
#11. Faraday's Law — Induced EMF
Element
Detail
Typical Problem
A coil of N turns and area A is placed in a magnetic field B that changes at rate dB/dt. Find the induced EMF. OR: A rod moves in a magnetic field. Find EMF.
Formula
EMF = -NdΦ/dt. Φ = BAcosθ. Motional EMF: ε = Blv
Shortcut
If B is changing but area is constant: EMF = NA(dB/dt). If area is changing (rod moving): EMF = Blv.
Common Mistake
Forgetting the cosθ term. If field is perpendicular to the plane of the coil, θ = 0° and cosθ = 1 (not sin).
Marks
2-3 marks
PYQ Frequency
2/3 years
#12. AC Circuits — LCR / Resonance
Element
Detail
Typical Problem
An LCR circuit with given L, C, R, and frequency. Find impedance, current, phase angle. OR: Find resonant frequency.
Formula
Z = √[R² + (X_L - X_C)²]. I = V/Z. Resonance: f₀ = 1/(2π√LC). At resonance: Z = R, I = V/R (maximum).
Shortcut
At resonance, X_L = X_C. Current is maximum. Power factor = 1. This is the most common "find the frequency" question.
Common Mistake
Wrong formula for X_L = ωL = 2πfL and X_C = 1/(ωC) = 1/(2πfC). Missing 2π in the conversion from f to ω.
Marks
3-5 marks
PYQ Frequency
2/3 years
Optics — Numericals #13-15
#13. Lens Formula / Mirror Formula
Element
Detail
Typical Problem
An object is placed at distance u from a convex lens of focal length f. Find image distance v and magnification.
Sign convention (CBSE): distances measured from optical centre/pole. Same direction as incident light = positive. Opposite = negative. For convex lens: u is always negative (object on left).
Common Mistake
Wrong sign convention. This is the #1 error in optics. Forgetting to put u as negative for objects on the left side.
Marks
2-3 marks
PYQ Frequency
3/3 years
#14. Lens Maker's Formula / Power of Lens Combination
Element
Detail
Typical Problem
Two thin lenses of focal lengths f₁ and f₂ are placed in contact. Find the equivalent focal length and power.
Formula
1/f = 1/f₁ + 1/f₂. Power P = 1/f (in metres) = P₁ + P₂. Lens maker: 1/f = (n-1)(1/R₁ - 1/R₂)
Shortcut
Power = 100/f (when f is in cm). Convex lens = +P. Concave lens = -P. For combination: just add powers.
Common Mistake
Mixing up focal length units (cm vs m). Power is in dioptres only when f is in metres.
Modern Physics: 10 problems (Photoelectric, de Broglie, Bohr, nuclear, decay)
#16-20
Day 13
Mixed paper: 10 numericals from all units
All
Day 14
SQP numericals only — solve under time pressure
All
Day 15
Weak areas revision — redo problems you got wrong
Targeted
Frequently Asked Questions
Q1. How many marks come from numericals in the Physics board paper?
25-30 marks out of 70 (theory paper). This includes MCQ-based numericals (1 mark each), short answer numericals (2-3 marks), and long answer numericals (5 marks). Numericals appear in EVERY section of the paper.
Q2. Can I get partial marks if my final numerical answer is wrong?
Yes. CBSE awards step-wise marks. If you write the correct formula (1 mark), substitute correctly (1 mark), but make a calculation error in the final step, you still get 2-3 marks out of 3-5. ALWAYS show your working. For more on how to write answers for maximum marks, see our presentation guide.
Q3. Should I memorize the shortcuts or derive formulas each time?
Memorize the shortcuts for quick problems (MCQs, 2-mark questions). For 3-mark and 5-mark problems, write the formula derivation because each step carries marks. Use the shortcut to verify your answer at the end.
Q4. Which unit has the easiest numericals?
Modern Physics. Photoelectric effect, de Broglie, and radioactive decay are formula-substitution problems. If you know the 5 formulas (#16-20), you can solve them in 2-3 minutes each.
Q5. What happens if I forget a formula during the exam?
During the first 15 minutes of reading time, write down all formulas you are afraid of forgetting on the last page of the answer sheet. This "formula dump" is allowed once writing begins. Start writing formulas from the moment the invigilator says "you may begin."
Q6. Are NCERT numericals enough or should I solve from other books?
NCERT solved examples + NCERT exercises cover 80% of board numerical types. For the remaining 20%, solve the SQP + 3 PYQ papers. You do not need to solve entire books like H.C. Verma or D.C. Pandey for board exams. Those are for JEE. For expected questions across other Class 12 subjects, also check the Maths expected questions.
